论文标题
保险投资组合中的可预见和不可预见的风险
Pricing foreseeable and unforeseeable risks in insurance portfolios
论文作者
论文摘要
在本手稿中，我们提出了一种定价保险产品的方法，不仅涵盖了传统风险，而且还涵盖了不可预见的风险。通过将泊松过程参数视为混合随机变量，我们捕获了可预见和不可预见的风险的异质性。为了说明，我们估计了葡萄牙保险公司的实际数据集的两个风险流的权重。为了计算溢价，我们将频率和严重性设置为属于线性指数家族的分布。在贝叶斯设置下，我们表明，在使用有限的共轭先验混合物时，可以通过后均值的混合物来估计溢价，并具有更新的参数，具体取决于索赔历史。我们通过选择重型分布来强调不可预见的趋势的风险。在估算了使用预期最大化算法涉及的分布参数之后，我们发现贝叶斯保费得出的保费比传统趋势更为反应。
In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity of foreseeable and unforeseeable risks. To illustrate, we estimate the weights for the two risk streams for a real dataset from a Portuguese insurer. To calculate the premium, we set the frequency and severity as distributions that belong to the linear exponential family. Under a Bayesian setup , we show that when working with a finite mixture of conjugate priors, the premium can be estimated by a mixture of posterior means, with updated parameters, depending on claim histories. We emphasise the riskiness of the unforeseeable trend, by choosing heavy-tailed distributions. After estimating distribution parameters involved using the Expectation-Maximization algorithm, we found that Bayesian premiums derived are more reactive to claim trends than traditional ones.
